Digital subscriber line (DSL) technologies provide a large bandwidth for digital communications over existing subscriber lines (e.g., copper pairs). When transmitting data over the subscriber lines, crosstalk interference can occur between the transmitted signals over adjacent lines, for example in a same or nearby bundle of lines. Crosstalk, including near end crosstalk (NEXT) and far end crosstalk (FEXT), may limit the performance of various DSL systems, such as those defined by existing standards including asymmetric DSL 2 (ADSL2), very high speed DSL (VDSL), very high speed DSL 2 (VDSL2), as well as G.fast which is a future standard to be issued by the International Telecommunication Union Telecommunication Standardization Sector (ITU-T) Study Group 15 (SG15).
In vectored DSL systems, an orthogonal probe sequence (sometimes also referred to as a pilot sequence) is used to estimate channel matrix. Take a VDSL2 system as an example: in order for an initializing VDSL2 transceiver unit on a remote side (VTU-R) modem to join in at the right bit index of an upstream probe sequence, the upstream probe sequence and its bit index may need to be transmitted from a VDSL2 transceiver unit on an operator side (VTU-O). Details regarding how an upstream probe sequence marker is transmitted from the VTU-O to the VTU-R can be found in the ITU-T G.993.5 Recommendation Section 10.3.3.5 headlined “Downstream Sync symbol and upstream pilot sequence markers”, which is incorporated herein by reference.
According to G.993.5 that defines vectoring protocols for FEXT cancellation in VDSL2 modems, per-tone frequency domain equalizers (FEQs) of a discrete multi-tone (DMT) demodulator may be primarily trained. In other vectored DSL systems such as G.fast, a used frequency band may be much higher and FEXT may be much stronger. Consequently, FEQ training using traditional methods, including least mean square (LMS), blind LMS (BLMS), and averaging, may work less effectively (e.g., convergence may take a long time).